In the textile industry slivers are transported from and to drawing frames as well as flyers and spinning machines with the aid of so-called sliver cans, cans for short. Following filling or emptying, each can is replaced by an empty or filled can. If necessary, the cans can be pulled or pushed individually or in groups on roller or sliding guides. Often, a large number of empty cans or full cans are transported, held and made available, and positioned for further transport between the drawing frames, flyers and spinning machines. It would therefore be advantageous if as many cans as possible could be simultaneously transported, held and positioned by means of the fewest possible driving devices.